Nadine Luedicke Dispenza^{1}, Robert Todd Constable^{2,3}, and Gigi Galiana^{4}

This work demonstrates the potential of FRONSAC, which adds oscillating nonlinear gradients to the Cartesian readout, for 3D accelerated imaging. In undersampled trajectories using either standard Cartesian encoding, CAIPI encoding, or WAVE-CAIPI encoding, significant further improvements are achieved when FRONSAC is applied in addition to these approaches.

FRONSAC, an acceleration strategy to improve undersampled image quality by applying small nonlinear gradient perturbations during the readout, has previously been demonstrated in 2D(1). Since the oscillating nonlinear gradients used in the FRONSAC approach varies spatially in 3 dimensions, it is expected that volumetric FRONSAC images will reduce undersampling artifacts in 2 dimensions.

FRONSAC encoding uses nonlinear gradients to modulate the *shape* of the sampling function in k-space, and it is distinct from linear
trajectories that change the *path* of
the sampling function in k-space. However, the oscillating nonlinear gradients
applied during readout make the FRONSAC technique appear similar to WAVE – a
technique with slew rate limited low frequency oscillating linear gradients(2). Likewise, the incoherent sampling created by
FRONSAC encoding is a feature shared by CAIPI, where the phase encoding of the
acquisition is modified to control the aliasing artifacts(3).

In this work, we show that each of these paths through k-space (Cartesian, CAIPI, and WAVE-CAIPI) are further enhanced by the addition of FRONSAC gradients. While CAIPI and WAVE-CAIPI provide a more efficient path through k-space, highly undersampled versions of these trajectories still leave significant gaps in k-space. The addition of nonlinear FRONSAC gradients improves the sampling of gaps in each trajectory, providing the best image quality from a highly undersampled scan.

1. Wang H, Tam LK, Constable RT, Galiana G. Fast rotary nonlinear spatial acquisition (FRONSAC) imaging. Magnetic Resonance in Medicine 2016;75(3):1154-1165.

2. Bilgic B, Gagoski BA, Cauley SF, Fan AP, Polimeni JR, Grant PE, Wald LL, Setsompop K. Wave-CAIPI for highly accelerated 3D imaging. Magn Reson Med 2014.

3. Breuer FA, Blaimer M, Heidemann RM, Mueller MF, Griswold MA, Jakob PM. Controlled aliasing in parallel imaging results in higher acceleration (CAIPIRINHA) for multi-slice imaging. Magnetic Resonance in Medicine 2005;53(3):684-691.

The
pulse sequence diagram for a 3D FRONSAC acquisition. Oscillating nonlinear
gradients are added during the readout where C3 and Z2 follow a sine waveform
while S3 follows a cosine waveform.

The
sum of the coil sensitivity profiles measured experimentally with a 32 channel
head coil. The limited sensitivity
in
the y direction is apparent in the sagittal slice.

Compared to an undersampled
Cartesian trajectory, both a CAIPI trajectory and a WAVE CAIPI trajectory
through k-space reduces undersampling
artifacts, as shown in the first column.
However, at high undersampling
factor, each of these methods leaves significant gaps in k-space. Adding nonlinear FRONSAC encoding to each of
these acquisitions, as shown in the second column, further improves undersampling,
with the best image quality achieved by a WAVE CAIPI linear trajectory enhanced
by nonlinear FRONSAC encoding. All
images are undersampled Ry*Rz=4x2.